Parameter: λ₁₂

Parameter: λ₁₃ Identified

Algebraic Equations:

σ₁₂λ₁₃-σ₂₃,
σ₁₁λ₁₃-σ₁₃

Single Door Criterion:

{1} ⊥ {3} | {}
{1} ⊥ {3} | {2}

Instrumental Variable:

2 | {}

Parameter: λ₁₄

Parameter: λ₃₄

Parameter: ω₁₁ Identified

Algebraic Equations:

-σ₁₁+ω₁₁

Parameter: ω₁₂

Parameter: ω₂₂

Parameter: ω₃₃ Identified

Algebraic Equations:

σ₁₃σ₂₃-σ₁₂σ₃₃+σ₁₂ω₃₃,
σ₁₃²-σ₁₁σ₃₃+σ₁₁ω₃₃

Parameter: ω₃₄

Parameter: ω₄₄

Total Effect of X₁ on X₄: λ₁₃λ₃₄+λ₁₄ Identified

Algebraic Equations:

σ₁₂λ₁₃λ₃₄+σ₁₂λ₁₄-σ₂₄,
σ₁₁λ₁₃λ₃₄+σ₁₁λ₁₄-σ₁₄

Back Door Criterion:

{1} ⊥ {3,4} | {}

Path-specific Effect of X₁ on X₄: λ₁₃λ₃₄

Vanishing Ideal

Constraint Set:

σ₁₄σ₂₃-σ₁₃σ₂₄,
σ₁₂σ₁₄-σ₁₁σ₂₄,
σ₁₂σ₁₃-σ₁₁σ₂₃

All constraints are determinantal

Trek-separation:

{1,2} ⊥ {1,3,4} | ({},{1})
{3,1,2} ⊥ {1,3,4} | ({3},{1})
{4,1,2} ⊥ {1,3,4} | ({4},{1})